I think we usually use a singular noun after "any"
"You can take any bus" means "You can take any one of the buses."
You could hardly get aboard more than one.
"I haven't any idea" is an expression in itself, so it has fixed the word "idea" in the singular.
But you can say, "I don't have any ideas to contribute to the Planning Committee" if that is what you mean.
Student or Learner